Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7082)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=4, b₁>=-23/4

For fixed z and a₁=4, b₁=-23/4

http://functions.wolfram.com/07.22.03.7082.01

Input Form

HypergeometricPFQ[{4}, {-(23/4), -(9/4)}, z] == (1/204417675) ((E^(2 Sqrt[z]) (204417675 + 63201600 z + 26611200 z^2 + 56770560 z^3 + 43223040 z^4 - 11083776 z^5 - 131072 z^6) - 128 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (-133875 + 267750 Sqrt[z] - 176400 z - 4200 z^(3/2) + 45600 z^2 + 9600 z^(5/2) + 512 z^3) Erf[Sqrt[2] z^(1/4)] + 128 Sqrt[2 Pi] z^(13/4) (-133875 - 267750 Sqrt[z] - 176400 z + 4200 z^(3/2) + 45600 z^2 - 9600 z^(5/2) + 512 z^3) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]